Melt the butter in a sauté pan on medium heat. Add the brown sugar and stir until melted. Add the balsamic vinegar and stir until it comes to a simmer. Core and slice the apples into ¼ inch slices; add to the pan in a single layer. Spoon the sauce over the apple slices and simmer for 2 minutes, then flip the slices. Cover and simmer until the slices are soft (when stuck with a fork they will slide off). Plate with a spoon of vanilla yogurt and garnish with a sprig of mint. A sprinkle of lemon zest and finely chopped mint are optional.